The long-time behavior of the standard ASEP height function relates to the KPZ fixed point and the KPZ equation. In this talk we consider "dynamic" variants of ASEP in which the rates of increase / decrease for the height function depend on the height in such a way as to have height reversion to a preferred level. Very little is known about the long-time behavior of this type of process. We prove an SPDE limit of the model under very weakly asymmetric scaling. Along the way, we also touch on dynamic ASEP 's Markov duality and relation to orthogonal polynomials.<br>
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This talk relates to a joint work with Alexei Borodin from last year (on the duality) and a new joint work with Konstantin Matetski and Promit Ghosal (on the SPDE limit).